The full reasoning can be found below the Sudoku.
Oct 02 - Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R2C7 is the only square in row 2 that can be <2>
R1C1 is the only square in row 1 that can be <2>
R3C2 is the only square in row 3 that can be <4>
R3C9 is the only square in row 3 that can be <7>
R5C4 is the only square in row 5 that can be <7>
R6C6 is the only square in row 6 that can be <2>
R7C6 is the only square in row 7 that can be <4>
R9C3 is the only square in row 9 that can be <4>
R8C2 is the only square in column 2 that can be <6>
R4C5 is the only square in column 5 that can be <6>
R4C7 is the only square in row 4 that can be <4>
R6C5 is the only square in row 6 that can be <4>
R1C9 is the only square in column 9 that can be <6>
Intersection of row 2 with block 1. The value <8> only appears in one or more of squares R2C1, R2C2 and R2C3 of row 2. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
R1C3 - removing <8> from <189> leaving <19>
Squares R1C3 and R1C7 in row 1 form a simple naked pair. These 2 squares both contain the 2 possibilities <19>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R1C4 - removing <19> from <1389> leaving <38>
R1C6 - removing <1> from <138> leaving <38>
Intersection of column 9 with block 9. The value <5> only appears in one or more of squares R7C9, R8C9 and R9C9 of column 9. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.
R7C8 - removing <5> from <13589> leaving <1389>
R8C8 - removing <5> from <135> leaving <13>
R8C3 is the only square in row 8 that can be <5>
R7C2 can only be <9>
R7C1 can only be <1>
R5C2 can only be <8>
R2C2 can only be <5>
R4C3 can only be <9>
R9C1 can only be <7>
R3C1 can only be <9>
R1C3 can only be <1>
R6C3 can only be <7>
R1C7 can only be <9>
R2C3 can only be <8>
R6C7 can only be <3>
R9C7 can only be <1>
R2C8 can only be <1>
R2C5 can only be <9>
R3C8 can only be <5>
R8C8 can only be <3>
R6C1 can only be <5>
R5C8 can only be <9>
R8C5 can only be <1>
R7C8 can only be <8>
R8C7 can only be <7>
R6C9 can only be <8>
R4C1 can only be <3>
R6C4 can only be <9>
R4C9 can only be <1>
R7C9 can only be <5>
R7C4 can only be <3>
R9C9 can only be <9>
R5C5 can only be <3>
R5C6 can only be <1>
R3C6 can only be <6>
R1C4 can only be <8>
R1C6 can only be <3>
R4C4 can only be <5>
R3C4 can only be <1>
R9C6 can only be <5>
R4C6 can only be <8>
R9C4 can only be <6>
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